The Mathematics Minor is designed for a student of any Discipline, other than Mathematics Major, who is interested in Mathematics and has some background in high-school and 12th-grade level mathematics (covered by MAT 142 – “Introductory Calculus”).
The objective of the Mathematics Minor program is to give students a solid foundation in the core topics in mathematics at an intermediate and advanced undergraduate level and to enable them to effectively use mathematics as a tool in their chosen Disciplines.
Students in the Mathematics Minor are expected to have a background in Calculus up to the 12th Standard level. In the absence of this, an equivalent course (e.g. MAT 110 – “Introductory College Maths” and MAT 142 – “Introductory Calculus”) will suffice to fulfil this prerequisite.
A minor in Mathematics requires 18 credits from six courses. The six courses are divided into two main parts.
The first part is the Mathematics Minor Core consisting of the following two courses:
- Multivariable Calculus (3 Credits)
- Linear Algebra (MAT 246) (3 Credits)
Calculus and linear algebra are fundamental to not only almost all the subfields of mathematics, but also in applications of mathematics in the natural sciences, engineering, economics, and management sciences. These topics, therefore, constitute the core of the Mathematics Minor.
The second part of the Mathematics Minor consists of four elective courses. The goal of this part is to provide students the opportunity to learn topics relevant to their Major Disciplines. It also offers students the flexibility to select the topics of their interest from a basket of certain advanced topics in Undergraduate Mathematics.
Mathematics Minor Part I: Mathematics Minor Core Courses
Outlines of the Mathematics Minor core courses are given below:
- Multivariable Calculus covers Parametric Equations, Vectors and the Geometry of Space, Vector-Valued Functions and Motion, Partial Derivatives, Multiple Integrals, Integrals, and Vector Fields.
- Linear Algebra covers Linear Equations, Matrix Algebra, Vector Spaces, Determinants, Eigenvalues and Eigenvectors, Diagonalization.
Mathematics Minor Part II: Mathematics Minor Elective Courses
Elective courses in Mathematics are either Standalone topics courses or a sequence of two courses covering an advanced topic in Undergraduate Mathematics, e.g., ‘Topology’ and ‘Basic Algebraic Topology’.
After completing the Mathematics Minor Core courses, i.e. from Part-I, the student should pick any four courses (worth 12 credits) from the following list of Standalone and Sequence courses. Often the second course in a sequence course requires the first course as a prerequisite, in such cases students must take the first course before taking the second course. In general, it is recommended and desirable, that students should take both the courses in a sequence course, but it is not mandatory.
- Introductory Algebra- Introduction to the Elements of Algebra for Undergraduates covering Groups, Rings and Fields and Elementary Applications (3 Credits)
- Differential Equations- First and Second-Order Ordinary Differential Equations, Systems of Differential Equations, Series Solutions, Qualitative Theory of Differential Equations, Introduction to PDE (3 Credits)
- Introduction to Numerical Analysis- A course in Numerical Analysis with a Laboratory at the Second and Third year Undergraduate Level (3 Credits)
- Advanced Linear Algebra- Orthogonality, Inner Product Spaces, Quadratic Forms, Sylvester’s Theorem of Inertia, Tensor Product, Multilinear Algebra (MAT 204), (3 Credits)
- Introductory Real Analysis- Properties of R Limits and Continuity, Derivative and Riemann Integral (3 Credits)
- Introduction to Topology- Topological spaces and continuous functions, connectedness, compactness, separation axioms, etc. (3 Credits)
- Probability- Fundamentals of Probability, Conditional Probability, Independence and Bayes’ Theorem, Random Variable, Discrete, Joint and Continuous Probability Distribution, etc. (STA 100) (3 Credits)
- Statistics- Descriptive Statistics, Probability Distributions, Sampling and Estimation, Hypothesis Testing, Correlation and Regression analysis, Design of experiments, etc. (STA 101) (3 Credits)
- Analysis: Basic Real Analysis-Basic Complex Analysis (6 Credits)
- Topology: Introduction to Topology-Basic Algebraic Topology (6 Credits)
- Calculus on Manifolds: Calculus in R^n-Calculus on Manifolds (6 Credits)
- Algebra: Introductory Algebra-Abstract Algebra (6 Credits)
- Number Theory: Abstract Algebra-Number Theory (6 Credits)
- Discrete Math: Discrete Mathematics-Combinatorics (6 Credits)
- Numerical Analysis: Basic Numerical Analysis-Advanced Numerical Analysis (6 Credits)
- Statistics: Introductory Probability and Statistics-Advanced Statistics (6 Credits)
- Geometry: Elementary Differential Geometry-Non-Euclidean Geometry (6 Credits)
- Advanced Linear Algebra: Advanced Linear Algebra-Advanced Algebra (6 Credits)
- Elective sequences from other disciplines (e.g., From Physics: Mathematical Physics/Relativity/Chaos, etc.) to be decided in consultation with that discipline (6 Credits)